The dispute - which began on Saturday - between the European states has prompted the United Nations (UN) to call for an investigation into the development.
On Saturday, Greek migration minister Notis Mitarachi tweeted a photo of the naked migrants, accusing Turkey of pushing them into Greece and stripping them naked before doing so.
The claim prompted Fahrettin Altun, the communications director of Turkey’s president Recep Tayyip Erdoğan, to accuse Greece of engaging in “fake news”.
On Monday, Turkey's foreign minister, Mevlüt Çavuşoğlu, again rejected the allegation and accused Athens of “shameless and reckless” behaviour.
He also took aim at European Union (EU) nations, accusing them of encouraging its fellow member, Greece, to “slander” Turkey.
Meanwhile, the spokesman for Greece’s government, Giannis Oikonomou, charged that Turkey was “continuing to openly instrumentalise migrants and even with unprecedented and unthinkable practices of barbarism”.
The exchange of accusations comes at a time of high tensions between the neighbouring countries, with both engaging in mutual accusations of airspace violations.
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Turkey has also accused Greece of militarising islands in the Aegean Sea - which would be a violation of international treaties - and threatening possible military action.
Mr Çavuşoğlu said: “To be able to appear right even when you are in the wrong like Greece - you need to be shameless and reckless. It’s only Greece that can achieve this.”
“It is natural that Greece... attempts to slander Turkey as its crimes increases,” he added.
Greek police said that its officers found the migrants naked on Friday, claiming some had “bodily injuries”.
The migrants are thought to have entered the country using plastic boats to cross the Evros River - known as Meric in Turkey - which forms a border between Greece and Turkey.
Turkey regularly accuses Greece of violently pushing back migrants entering the country by land and sea, and its coast guard shares videos of such pushbacks.
Elsewhere, Greece blames Turkey, which hosts the largest number of refugees in the world, of “pushing forward” migrants to put pressure on the EU.